科研之友
微信
新浪微博
Facebook
分享链接
摘要
The meshfree point interpolation method (PIM) based on polynomial function is presented for the static analysis of spatial general shell structures. The formulation of the discrete system equations is derived from stress resultant geometrically exact shell theory of shear flexible shells based on the Cosserat surface. The PIM technique constructs its interpolation functions through a set of arbitrarily distributed points in the problem domain and its shape function has the delta function property. Hence, the implementation of essential boundary conditions can be imposed with ease as in conventional finite element method. An improved matrix triangularization algorithm (NITA) is proposed to obtain proper node enclosure and basis selection in order to overcome the singularity problem in the point interpolation method using a polynomial basis. It is found that the shape functions are generally not compatible to ensure the compatibility of the solution and lead to non-conforming PIM (NPIM) when the energy principles are used to formulate PIM. To obtain compatible shape functions, the enforcement of compatibility is needed along the common edges of the background cells in the problem domain and a background cell-based nodal selection is utilized, which lead to conforming PIM (CPIM). Both NPIM and CPIM are evaluated in the paper. Several benchmark problems for shells are analyzed to demonstrate the validity and efficiency of the NPIM and CPIM. The phenomena of shear locking and membrane locking are illustrated by showing the membrane and shear energies as fractions of the total energy. The convergences and performances are investigated for both conforming and non-conforming PIMs. It is also shown that the NPIM and CPIM with the improved NITA are very easy to implement and very efficient in constructing shape functions in comparison with the Element-Free Galerkin method.
- 出版日期2007
- 单位南阳理工学院
